Section 4: FPS21 Modulus Inputs and Backcalculation Methodology

4.1 Overview of Modulus Inputs

Each material layer used in the structure will have a modulus
input that shall characterize the average seasonal stiffness of
that material over the course of the year. The construction process, inherent
material variability (initially and over time), and effects of environment
(moisture and temperature) and traffic loading will typically introduce
considerable variance about the average value. Modulus inputs for
HMA are based on a temperature of 77°F.

Overestimating this material property can result in a structure
with poor permanent deformation performance and may subject the
surface to early fatigue, while underestimating can result in an uneconomical
pavement.

Additionally, materials that have an average in situ modulus
in one circumstance may have a different average modulus if placed
in another environment. This is particularly true of unbound base material;
the modulus can be significantly influenced by the confinement provided
by the layers above or below, absence of paved shoulders, or by
the amount of moisture infiltrating the structure if the materials
are moisture susceptible.

In evaluating a design that consists of layers that were pre-existing
(including the subgrade), the falling weight deflectometer (FWD)
is indispensable in determining what stiffnesses (through backcalculation)
these layers can contribute to the new structure. Proposed virgin
and reclaimed material moduli will require knowledge by the designer
(preferably through past use and subsequent evaluation), tempered
by the specifics of the current project.

Studies conducted on perpetual pavements indicate that stone-on-stone
designed Superpave hot-mixes and thick composite HMA structures,
using any type of HMA, have much stiffer in-place moduli values
than conventional thinner surfaced HMA structures. Laboratory and
field testing continues on these mixes to establish stiffness-temperature
curves and better define “design” stiffness values by type, if necessary.

All backcalculated material modulus values are manually entered
into their respective fields (values are not read from the MODULUS
backcalculation summary file).

4.2 Virgin and Modified-in-Place Materials

Below is a partial listing of typical design moduli by material
type for virgin or modified-in-place materials to be used in FPS
21. For materials not listed, contact MNT – Pavement Asset Management
for recommendations.

If historic data not available, modulus
shall be no greater than 3-4 times the subgrade modulus or use FPS default, whichever
is lower. Typical range 40-70 ksi.

0.35

In general, a finer graded base will
have lower moduli than one that is a coarser gradation. As angularity
and soundness of particles decrease, modulus will decrease to the
lower end of the scale. Limiting the minus 200 clay fraction will
improve resistance to moisture damage.

Use Tex-121-E or Tex-120-E, Parts
1, to establish optimum lime or cement content. Long-term stiffness
improvement will depend on concentration used and affinity of subgrade
material to undergo permanent chemical bonding. For cases when a
subgrade will be treated (2-3% lime) to provide a working platform
for construction equipment and a platform to improve compactive
effort of the overlying layers, this layer shall not
be accounted for in the structural design.

Priority should be to use the project-specific backcalculated
subgrade modulus. Defaults by county are available in the FPS design program.
Typical range is 8-20 ksi.

0.35 - 0.45

Use of a backcalculated modulus is
preferred. FPS 21 defaults to the average county subgrade modulus
taken from a limited number of tests. For new highway construction
on a new right-of-way, deflection testing on an adjacent highway,
or intersecting highways can provide data for backcalculation. Alternatively, elastic
modulus correlations to field or laboratory derived CBR or the program
default may be used. Wetter or more highly plastic materials warrant
higher Poisson ratios.

4.3 Backcalculation Methodology

This procedure is used to determine modulus values for in
situ pavement materials when these materials are used as is (unmodified)
in FPS design. TxDOT currently uses version 6.1 of the MODULUS software
for backcalculation of deflection data collected by the FWD. Version
6.1 is comparable to version 6.0; the main difference is the ability
to read current Dynatest R80 formatted data files that have GPS
locations embedded. The software (v 6.1) and user’s manual (v 6.0)
in PDF document format are available through the MNT
Engineering
applications link to the TTI on-line pavement design training
site. Also, basic operation and discussion of inputs, cautions,
and example problems is presented in the Flexible Pavement
Rehabilitation Strategies training course and Flexible
Pavement Design workshop.

The raw deflection file, pavement layer thicknesses, layer
Poisson ratios, probable layer moduli ranges, and asphalt temperatures
at the time of testing are all required inputs to perform backcalculation.
The backcalculation process works on the assumption that the pavement
structure can be modeled as a linear-elastic layered system. If
the parameters of layer thickness, deflection, and Poisson ratio
are known, the modulus can be approximated. A likely range of “probable”
layer moduli provided by the program user facilitates the process
by forming the basis of a small internal database against which
mathematically generated deflection bowls are compared to the actual
measured deflection bowl by the software. Once a reasonable match
is made, the moduli that allow this match are reported as the individual
layer moduli. In addition, the program reports a depth to stiff layer
or bedrock.

4.3.1. Backcalculation Limitations and Adjustments

There are precautions and limitations to the backcalculation
procedure that the user must consider. In the end, engineering judgment
will be needed to decide on the veracity of solutions generated. The
following are some pointers when using MODULUS 6.1:

The modulus for
layers thinner than 3.0 in. cannot be backcalculated. This situation
arises most often for thin-surfaced flexible pavements. The user
must assign a reasonable modulus to this layer (minimum and maximum
are input as the same value in the program) based on thickness, level
of distress, temperature, etc.

The surface layer is always the layer
that the load plate is in contact with, so a thickness must be entered.
Where the surface is a bituminous surface treatment, it is allowable
to use a nominal thickness, such as 0.5 in., and assign a nominal
modulus, such as 200 ksi. Alternatively, the surface treatment can
be combined with the underlying layer as the “surface,” reducing
the total number of layers by one. In determining the seed moduli
range for the surface, MODULUS assumes the layer is HMA and automatically
fills the min/max seed values in accordance with the temperature
posted in the Asphalt Temp cell. Where non-bituminous materials
are the surface during testing, the user must insert seed values
commensurate with the type of material tested.

The maximum number of layers for which
the modulus can be backcalculated is four (one of which is always
the natural subgrade) in MODULUS 6.1. For circumstances where more
layers are known to exist, the user must either consolidate or ignore
layers. Consolidation is recommended for materials that are more
likely to have a similar modulus and shear strength properties (i.e.,
different types of HMA, or flex base over reclaimed base). Ignoring
layers may be reasonable in certain cases where the material’s contribution
to the overall stiffness of the structure is minimal (i.e., “foundation
course,” or lime treated subgrade – constructed as a working platform).

There are times when a more reasonable
solution is obtained modeling your pavement structure as a 3-layer
system, even if you know there are four layers present. This situation
may develop for a number of reasons, such as variable stabilization
(leaching), variable depth to bedrock, etc.

A check of reasonableness in the solutions
generated shall be made. Reasonableness is more related to the in-place
stiffness characteristics of the layers being modeled and not necessarily to
the size of the average errors reported by the software in comparing
the mathematically generated bowls to the measured bowls. While
the 4-layer solution will generally give lower overall errors, the
backcalculated material moduli may be unrealistic with respect to
the in-place material, and the variability of reported moduli may
be excessive (coefficient of variation 100% or greater). When there
is doubt of reasonableness, the user should perform backcalculation
runs using both 3- and 4-layer solutions (employing guidelines given
in the third bullet). Additional field testing, such as with the
dynamic cone penetrometer (DCP) along with engineering judgment,
is necessary to ensure a valid, reliable solution.

A check of the MODULUS summary table shall
be made to detect outliers that skew the average value reported.
Outliers may be the result of full-depth patches (different pavement structure)
or very weak areas.

For the purpose of using MODULUS-reported
values as input to FPS 21, adjustment of the average modulus shall
be considered; otherwise the performance of any pavement design
solution based on these inputs could be jeopardized. As a rule-of-thumb,
consider removing values that exceed one standard deviation from
the unadjusted average, and then re-average. This should always
be done for modulus values that are much higher than values that
are more typical for the section. Consideration can be given to
eliminating very low values only if the intention
is to include a bid item for repair of weak areas (i.e., Item 351,
“Flexible Pavement Structure Repair,” or Item 354, “Planing and
Texturing Pavement”) as part of the job.

Shallow bedrock (typically less than 60
in. deep) will almost always result in underestimation of the subgrade
modulus and overestimation of the flexible base modulus and produce
very high average error (> 20%). The recommended workaround is to
fix the depth to bedrock (DTB) at 120 in. or, alternatively, 240
in. if the solution using the program-generated DTB produces suspect
subgrade/base moduli. Another clue that the default solution is
suspect would be if the ratio of the flexible base modulus (unstabilized
layers only) to the subgrade modulus is very high (> 5). If the
user opts to fix the calculated DTB to a value in the 120- to 240-in. range,
then this user-selected value must also be used in FPS 21 design.

MODULUS can perceive a shallow DTB in
high water table situations (water is incompressible) as can be
the case in east Texas. It may be beneficial to override the program-generated DTB
value by using a fixed value of 120 in. Again, check the generated
subgrade/base moduli values for reasonableness.

Soft upper subgrade can also lead to high
errors in the backcalculation process. In these cases, use a 4-layer
solution where the soft portion of the subgrade is modeled as the
subbase layer (fix depth at 12 in.) to provide better fit and more
realistic backcalculated values for the base and deep subgrade.
A check can be made in MODULUS using the Boussinesq procedure to evaluate
how the subgrade modulus varies with depth. Verification with a
dynamic cone penetrometer (DCP) may be warranted.

4.3.2 Modulus Correction Factors

In addition to adjustments made to backcalculated average
modulus values for outliers in the deflection data set, correction
factors must be applied to backcalculated:

4.3.2.1. HMA values

FPS 21 considers the modulus of bituminous materials only
at the reference temperature of 77˚F. Since FWD data are rarely
collected at the reference temperature, corrections must be made
for FPS input. Two methods are suggested:

Use the formula CF
= T2.81/200,000,
where CF is the correction factor to be multiplied by the backcalculated
HMA modulus (adjusted for outliers), and T is the average temperature
over the time the FWD survey was made, or

Use the Modulus Temperature Correction
Program
(MTCP).
MTCP can use the surface temperatures measured at each deflection
location and, together with the previous day’s average temperature
(available at weather underground
http://www.wunderground.com/history/),
predict the in-pavement temperature and compute the temperature
adjusted modulus. Again, outliers must be removed from the calculated
average.

4.3.2.2. Flexible Base values

Performance models in FPS 21 expect a 10.0-in. thick flexible
base. For backcalculated moduli of base layers that have a different
thickness, multiplication correction factors in the following table should
be used: